Given the PMF
(a)
(b) The CDF is defined as
, so that
It follows that
(c) Expectation is defined as
We have
(d) First compute the second moment of X, which is defined as
We get
Variance is defined as
so it follows that
(e) Not sure what this part has to do with the rest of the question. At any rate, if Y is a random variable following a Poisson distribution with λ = 3, then Y has a PDF of
Then